Distorted fingerprint matching using pose and minutia grouping

ABSTRACT

A list of possible mated minutiae in a reference fingerprint and a search fingerprint is identified. The list of possible mated minutiae is divided into different groups of mated minutiae using pose grouping based on rigid transformation parameters. For each group, the possible mated minutiae are filtered to get a set of consistent mated minutiae pairs having similar rigid transformation. The topological consistency between groups is determined. If any two groups are topologically consistent to each other, they are merged to form a (virtual) larger group. A non-linear transformation parameters are estimated from the the mated minutiae in the merged group. The overall similarity of mated and non-mated minutiae in the overlapping area is determined after non-linear alignment of the two fingerprints, and the maximum similarity is output as the final similarity score between two fingerprints.

FIELD

This disclosure generally relates to fingerprint identification systems.

BACKGROUND

Pattern matching systems such as ten-print or fingerprint matchingsystems play an important role in criminal and civil applications. Forexample, fingerprint identification is often used to identify and tracksuspects and in criminal investigations. Similarly, fingerprintverification is used in in civil applications to prevent fraud andsupport other security processes.

SUMMARY

In general, the matching of distorted fingerprints pose severalchallenges to fingerprint identification and matching technologies. Forinstance, distortions can impact matching accuracy because thedistortions may change both the geometric locations and orientations ofminutiae.

Aspects of this disclosure address the above-noted deficiencies andprovide improved matching to the distorted fingerprints. According tosome implementations, a list of possible mated minutiae in a referencefingerprint and a search fingerprint is identified. The list of possiblemated minutiae is divided into different groups of mated minutiae usingpose grouping based on rigid transformation parameters. For each group,the possible mated minutiae are filtered to get a set of consistentmated minutiae pairs having similar rigid transformation. Thetopological consistency between groups is determined. If any two groupsare topologically consistent to each other, they are merged to form a(virtual) larger group. Non-linear transformation parameters areestimated from the mated minutiae in the merged group. The overallsimilarity of mated and non-mated minutiae in the overlapping area isdetermined after non-linear alignment of the two fingerprints, and themaximum similarity is output as the final similarity score between twofingerprints.

Aspects of the implementations disclosed in this specification includesystems and methods for matching distorted fingerprints. The method,executed at least in part by one or more processors, includes selecting(i) one or more search minutiae of a search fingerprint, and (ii) one ormore reference minutiae of a reference fingerprint. For each searchminutia included in the one or more search minutiae, a correspondingreference minutia from the one or more reference minutiae is identified.The corresponding reference minutia has a similarity to the searchminutia that satisfies a similarity threshold. The method furtherincludes determining one or more groups of the one or more searchminutiae in the search fingerprint and the one or more referenceminutiae in the reference fingerprint that match the each other,determining one or more matches between the groups based on atopological consistency between two groups, for each matched pair ofgroups, merging, by the one or more processors, minutiae in the pair ofgroups, and performing a non-linear transformation on the one or moresearch minutiae of the search fingerprint.

Implementations may each optionally include one or more of the followingfeatures. For instance, in some implementations, the method furtherincludes in response to performing the non-linear transformation,determining similarity levels associated with the selected one or moresearch minutiae and the selected one or more reference minutiae. Thesimilarity levels include similarities of matched and non-matchedminutiae in an overlapping area of the selected one or more searchminutiae and the selected one or more reference minutiae. The methodfurther includes determining, as a similarity between the searchfingerprint and the reference fingerprint, the best similarity levelamong all groups having topologically consistent group pairs.

In some implementations, performing a non-linear transformation includesdetermining parameters for a Thin-Plate Spline (TPS) model and applyingthe determined parameters to the one or more search minutiae of thesearch fingerprint to perform the non-linear transformation.

In some implementations, the method further includes determining whethera group is a merged group or a non-merged group, and performing rigidtransformation on the minutiae included in the group in response todetermining that the group is a non-merged group.

In some implementations, the method further includes determining thatthe group is a merged group. Performing the non-linear transformationincludes performing non-linear transformation on the one or more searchminutiae of the search fingerprint in response to determining that thegroup is a merged group.

In some implementations, each group includes two or more mated minutiaepairs having rigid transformation parameters that satisfy a thresholdlevel of similarity.

In some implementations, the one or more groups of the one or moresearch minutiae in the search fingerprint and the one or more referenceminutiae in the reference fingerprint are determined based on values ofthe rigid transformation parameters.

Other aspects include corresponding methods, systems, apparatus,computer-readable storage media, and computer programs configured toimplement the above-noted embodiments.

The above-noted aspects and implementations further described in thisspecification may offer several advantages. For example, advantages ofthe implementations disclosed in this specification include one or moreof: (a) improved accuracy in fingerprint matching systems; (b) reductionof false positive and false negative rates; and (c) increased speed offingerprint matching.

The details of one or more implementations are set forth in theaccompanying drawings and the description below. Other features andadvantages will become apparent from the description, the drawings, andthe claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A depicts a block diagram of an exemplary computing device in anautomatic fingerprint identification system.

FIG. 1B depicts a block diagram of an exemplary feature extractionprocess in an automatic fingerprint identification system.

FIG. 2 is an exemplary illustration of geometric relationships between aparticular minutia and a neighboring minutia.

FIG. 3 is a graphical illustration of the relationships represented inan exemplary octant feature vector (OFV).

FIG. 4 depicts an exemplary process of generating an octant featurevector (OFV).

FIG. 5 depicts an exemplary process of calculating similarity betweentwo minutiae.

FIGS. 6A and 6B depict an exemplary process for matching distortedfingerprints.

FIG. 7 depicts exemplary reference and search fingerprints with matedminutiae.

FIG. 8 depicts exemplary reference and search fingerprints with matedminutiae.

FIG. 9 depicts two groups of mated minutiae.

FIG. 10 depicts exemplary reference and search fingerprints with matedminutiae after non-linear and robust transformations.

In the drawings, like reference numbers represent corresponding partsthroughout.

DETAILED DESCRIPTION

Advancements have been made in fingerprint identification systems.However, matching distorted fingerprints is still a challenge. In somecases, nonlinear distortions of fingerprint may be unavoidable whencapturing the images of a live finger with a two-dimensional (2-D)contact sensor because of the elasticity of the skin, contact pressure,finger displacement, skin moisture content, and/or sensor noise. In manyinstances, fingerprints are obtained from latent images and include onlypartial prints having reduced, blurred, noisy, or distorted fingerprintregions. Improvements in fingerprint identification systems for matchingdistorted fingerprints are needed to reduce false positive and falsenegative results of fingerprint matching.

Implementations of methods and systems for matching distortedfingerprints are described with reference to FIGS. 1A-10.

FIG. 1A is a block diagram of an exemplary automatic fingerprintidentification system (AFIS) 100. Briefly, the automatic fingerprintidentification system 100 may include a computing device including amemory device 110, a processor 115, a presentation interface 120, a userinput interface 130, and a communication interface 135. The automaticfingerprint identification system 100 may be configured to facilitateand implement the methods described is this specification. In addition,the automatic fingerprint identification system 100 may incorporate anysuitable computer architecture that enables operations of the systemdescribed throughout this specification.

The processor 115 may be operatively coupled to memory device 110 forexecuting instructions to implement the methods described is thisspecification. In some implementations, executable instructions arestored in the memory device 110. For instance, the automatic fingerprintidentification system 100 may be configurable to perform one or moreoperations described by programming the processor 115. For example, theprocessor 115 may be programmed by encoding an operation as one or moreexecutable instructions and providing the executable instructions in thememory device 110. The processor 115 may include one or more processingunits, e.g., without limitation, in a multi-core configuration.

The processor 115 may include one or more processing units, e.g., in amulti-core configuration. The term processing unit, as used herein,refers to microprocessors, microcontrollers, reduced instruction setcircuits (RISC), application specific integrated circuits (ASIC), logiccircuits, and any other circuit or device capable of executinginstructions to perform functions described herein.

The memory device 110 may be one or more devices that enable storage andretrieval of information such as executable instructions and/or otherdata. The memory device 110 may include one or more tangible,non-transitory computer-readable media, such as, without limitation,random access memory (RAM), dynamic random access memory (DRAM), staticrandom access memory (SRAM), a solid state disk, a hard disk, read-onlymemory (ROM), erasable programmable ROM (EPROM), electrically erasableprogrammable ROM (EEPROM), and/or non-volatile RAM (NVRAM) memory. Theabove memory types are exemplary only, and are thus not limiting as tothe types of memory usable for storage of a computer program.

The memory device 110 may be configured to store a variety of dataincluding, for example, matching algorithms, scoring algorithms, scoringthresholds, perturbation algorithms, fusion algorithms, virtual minutiaegeneration algorithms, minutiae overlap analysis algorithms, and/orvirtual minutiae analysis algorithms. In addition, the memory device 110may be configured to store any suitable data to facilitate the methodsdescribed throughout this specification.

The presentation interface 120 may be coupled to processor 115. Forinstance, the presentation interface 120 may present information, suchas a user interface showing data related to fingerprint matching, to auser 102. For example, the presentation interface 120 may include adisplay adapter (not shown) that may be coupled to a display device (notshown), such as a cathode ray tube (CRT), a liquid crystal display(LCD), an organic LED (OLED) display, and/or a hand-held device with adisplay. In some implementations, the presentation interface 120includes one or more display devices. In addition, or alternatively, thepresentation interface 120 may include an audio output device (notshown), e.g., an audio adapter and/or a speaker.

The user input interface 130 may be coupled to the processor 115 andreceives input from the user 102. The user input interface 130 mayinclude, for example, a keyboard, a pointing device, a mouse, a stylus,and/or a touch sensitive panel, e.g., a touch pad or a touch screen. Asingle component, such as a touch screen, may function as both a displaydevice of the presentation interface 120 and the user input interface130.

In some implementations, the user input interface 130 may represent afingerprint scanning device that is used to capture and recordfingerprints associated with a subject (e.g., a human individual) from aphysical scan of a finger, or alternately, from a scan of a latentprint. In addition, the user input interface 130 may be used to create aplurality of reference records.

A communication interface 135 may be coupled to the processor 115 andconfigured to be coupled in communication with one or more other devicessuch as, for example, another computing system (not shown), scanners,cameras, and other devices that may be used to provide biometricinformation such as fingerprints to the automatic fingerprintidentification system 100. Such biometric systems and devices may beused to scan previously captured fingerprints or other image data or tocapture live fingerprints from subjects. The communication interface 135may include, for example, a wired network adapter, a wireless networkadapter, a mobile telecommunications adapter, a serial communicationadapter, and/or a parallel communication adapter. The communicationinterface 135 may receive data from and/or transmit data to one or moreremote devices. The communication interface 135 may be also beweb-enabled for remote communications, for example, with a remotedesktop computer (not shown).

The presentation interface 120 and/or the communication interface 135may both be capable of providing information suitable for use with themethods described throughout this specification, e.g., to the user 102or to another device. In this regard, the presentation interface 120 andthe communication interface 135 may be used to as output devices. Inother instances, the user input interface 130 and the communicationinterface 135 may be capable of receiving information suitable for usewith the methods described throughout this specification, and may beused as input devices.

The processor 115 and/or the memory device 110 may also be operativelycoupled to one or more databases 150. The one or more databases 150 maybe any computer-operated hardware suitable for storing and/or retrievingdata, such as, for example, pre-processed fingerprints, processedfingerprints, normalized fingerprints, extracted features, extracted andprocessed feature vectors such as octant feature vectors (OFVs),threshold values, virtual minutiae lists, minutiae lists, matchingalgorithms, scoring algorithms, scoring thresholds, perturbationalgorithms, fusion algorithms, virtual minutiae generation algorithms,minutiae overlap analysis algorithms, and virtual minutiae analysisalgorithms.

In some implementations, the database 150 may be integrated into theautomatic fingerprint identification system 100. The automaticfingerprint identification system 100 may include one or more hard diskdrives that represent the database 150. For example, the database 150may include multiple storage units such as hard disks and/or solid statedisks in a redundant array of inexpensive disks (RAID) configuration. Insome implementations, the database 150 may include a storage areanetwork (SAN), a network attached storage (NAS) system, and/orcloud-based storage. In some implementations, the database 150 may beexternal to the automatic fingerprint identification system 100 and maybe accessed by a storage interface (not shown). For instance, thedatabase 150 may be used to store various versions of reference recordsincluding associated minutiae, octant feature vectors (OFVs) andassociated data related to reference records.

The computing device may include or be connected to access points,storage systems, cloud systems, modules, one or more databases includingone or more media databases, and servers including one or more networkservers such as a computing device. In some implementations, the one ormore network servers may include any suitable electronic device coupledto the one or more networks, including but not limited to a personalcomputer, a server computer, a series of server computers, a minicomputer, and a mainframe computer, or combinations thereof. The one ormore network servers may also include an application server, a webserver, or a series of servers, running a network operating system,examples of which may include but are not limited to Microsoft® Windows®Server, Novell® NetWare®, or Linux®. The one or more network servers maybe used for and/or provide cloud and/or network computing and mediaprovision services. Although not shown in the figures, the server mayhave connections to external systems providing messaging functionalitysuch as e-mail, SMS messaging, text messaging, and otherfunctionalities, such as advertising services, search services, etc. Insome implementations, the one or more networks may include a cloudsystem that may provide Internet connectivity and other network-relatedfunctions. For example, the cloud system may provide storage servicesfor at least a portion of the data transmitted between components of thesystem.

Communicatively coupled components may be in communication through beingintegrated on the same printed circuit board (PCB), in communicationthrough a bus, through shared memory, through a wired or wireless datacommunication network, and/or other means of data communication. Datacommunication networks referred to herein may be implemented usingTransport Control Protocol/Internet Protocol (TCP/IP), User DatagramProtocol (UDP), or the like, and the underlying connections may comprisewired connections and corresponding protocols, for example, Institute ofElectrical and Electronics Engineers (IEEE) 802.3 and/or wirelessconnections and associated protocols, for example, an IEEE 802.11protocol, an IEEE 802.15 protocol, and/or an IEEE 802.16 protocol.

Feature Extraction

In general, feature extraction describes the process by which theautomatic fingerprint detection system 100 extracts a list of minutiaefrom each of reference fingerprint, and the search fingerprint. A“minutiae” represents features of a fingerprint and may be used incomparisons of a reference fingerprint to a search fingerprint todetermine a fingerprint match. For example, common types of minutiae mayinclude, for example, a ridge ending, a ridge bifurcation, a shortridge, an island, a ridge enclosure, a spur, a crossover or bridge, adelta, or a core.

FIG. 1B is a block diagram of an exemplary feature extraction process150. As shown, after receiving an input fingerprint 104, the automaticfingerprint detection system 100 initially identifies a set of features112 within the fingerprint, generates a list of minutiae 114, andextracts a set of feature vectors 116. For instance, the automaticfingerprint detection system 100 may generate a list of minutia 114 foreach of the reference fingerprint (or “reference record”) and a searchfingerprint (or “search record”).

In some implementations, the feature vectors 116 may be described usingfeature vector that is represented Mf_(i)=(x_(i),y_(i),θ_(i)). Thefeature vector Mf_(i) includes a minutia location that is defined bycoordinate geometry such as (x_(i),y_(i)), and a minutiae direction thatis defined by the angle θ_(i)∈[0,2π]. In some implementations, furtherminutiae characteristics such as, quality, ridge frequency, and ridgecurvature may also be used to describe feature vector Mf_(i). Theextracted feature vectors may be used to generate octant feature vectors(OFVs) for each of identified minutia within the search and referencefingerprints.

Octant Feature Vector (OFV) Overview

The automatic fingerprint identification system 100 may compare thesearch and reference records by generating and comparing feature vectorsassociated with minutiae that are extracted from the search andreference records, respectively. For instance, as described in moredetail with reference to FIG. 5 below, octant feature vectors (OFVs) maybe used to define attributes of the extracted minutiae. In someimplementations, other minutiae descriptors may be used.

OFVs encode geometric relationships between particular minutiae and thenearest neighboring minutiae to the particular minutiae in a particularsector (referred to as the “octant neighborhood”) of an octant. Eachsector of the octant used in an OFV spans 45 degrees of a fingerprintregion. The nearest neighboring minutiae may be assigned to one sectorof the octant based on their orientation difference. The geometricrelationship between a particular minutia and its nearest minutia ineach octant sector may be described by relative features including, forexample, distance between the minutiae and the orientation differencebetween minutiae. The representation achieved by the use of an OFV isinvariant to rigid transformation.

OFV Generation

The automatic fingerprint identification system 100 may generate anoctant feature vector (OFV) for each minutia of the features extracted.Specifically, the automatic fingerprint identification system 100 maygenerate OFVs encoding the distance and the orientation differencebetween the particular minutiae and the nearest neighbor in each ofeight octant sectors. In some implementations, the automatic fingerprintidentification system 100 may generate feature vectors with differentnumbers of sectors.

FIG. 2 is an exemplary illustration of geometric relationships between aparticular minutia 210 and a neighboring minutia 220. The geometricrelationships may be used to construct a rotation and translationinvariant feature vector that includes relative attributes(d_(ij),α_(ij),β_(ij)) between the particular minutia 210 and theneighboring minutia 220.

As depicted in FIG. 2, the automatic fingerprint identification system100 may compute a Euclidean distance 230 between the particular minutia210 and the neighboring minutia 220, a minimum rotation angle 240 forthe neighboring minutia, and a minimum rotation angle 250 for theparticular minutia 210. In addition, the automatic fingerprintidentification system may compute a ridge count 260 across theparticular minutia 210 and the neighboring minutia 220.

Specifically, the rotation and translation invariant feature vector maybe represented as vector 1 (represented below). In some implementations,an OFV is created to describe the geometric relationship between.Further, M_(i) represents the particular minutia and M_(j) representsthe nearest neighbor minutiae in one of the octant sectors. The OFV foreach sector may be described in the given vector from vector 1:

Vector 1: (d_(ij),α_(ij),β_(ij)),

-   -   where d_(ij) denotes the Euclidean distance 230,    -   where α_(ij)=(θ_(i),θ_(j)) denotes the minimum rotation angle        240 required to rotate a line of direction θ_(i) in a particular        direction to make the line parallel with a line of direction        θ_(j), and    -   where β_(ij)=λ(θ_(i),∠(M_(i),M_(j))) denotes the minimum        rotation angle 250, where ∠(M_(i),M_(j)) denotes the direction        from the particular minutia 210 to the neighboring minutia 220,        and where λ(a,b) denotes the same meaning as defined in α_(ij)

Because each element calculated in the feature vector is a relativemeasurement between the particular minutia 210 and the neighboringminutia 220, the feature vector is independent from the rotation andtranslation of the fingerprint. Elements 230, 240, and 250 may bereferred to as relative features and are used to compute the similaritybetween pair of particular minutia 210 and the neighboring minutia 220.In some implementations, other minutiae features such as absolutefeatures may additionally or alternatively be used by the automaticfingerprint identification system 100 to weigh the computed similarityscore between a pair of mated minutiae that includes particular minutia210 and the neighboring minutia 220.

FIG. 3 is a graphical illustration of the relationships represented inan exemplary octant feature vector (OFV) 300. The OFV 300 may begenerated for a particular minutia 310, which corresponds to theparticular minutia 210 shown in FIG. 2. The OFV 300 representsrelationships between the particular minutiae 310 and its nearestneighboring minutiae 322, 332, 342, 352, 362, 372, 382, and 392 insectors 320, 330, 340, 350, 360, 370, 380, and 390, respectively.However, the graphical illustration of OFV 300 does not depict thedetails of the geographic relationships, which are described withinrespect to FIG. 2. Although FIG. 3 indicates a neighboring minutiawithin each octant sector, in some instances, there may be noneighboring minutiae within a particular sector. In such instances, theOFV for the particular sector without a neighboring minutia is set tozero. Otherwise, because the neighboring minutiae 322, 332, 342, 352,362, 372, 382, and 392 may not overlap with particular minutiae 310, theOFV is greater than zero.

FIG. 4 is an exemplary process 400 of generating an octant featurevector (OFV). Briefly, the process 400 may include identifying aplurality of minutiae from the input fingerprint image (410), selectinga particular minutia from the plurality of minutiae (420), defining aset of octant sectors for the plurality of minutiae (430), assigningeach of the plurality of minutiae to an octant sector (440), identifyinga neighboring minutiae to the particular minutia for each octant sector(450), and generating an octant feature vector for the particularminutia (460).

In more detail, the process 400 may include identifying a plurality ofminutiae from the input fingerprint image (410). For instance, theautomatic fingerprint identification system 100 may receive the inputfingerprint 402 and generate a list of minutiae 412 using the techniquesdescribed previously with respect to FIG. 1B.

The process 400 may include selecting a particular minutia from theplurality of minutiae (420). For instance, the automatic fingerprintidentification system 100 may select a particular minutiae within thelist of minutiae 412.

The process 400 may include defining a set of octant sectors for theplurality of minutiae (430). For instance, the automatic fingerprintidentification system 100 may generate a set of octant sectors 432 thatinclude individual octant sectors k₀ to k₇ as shown in FIG. 4. The setof octant sectors 432 may be generated in reference to the particularminutia that is selected in step 420.

The process 400 may include assigning each of the plurality of minutiaeto an octant sector (440). For instance, the automatic fingerprintidentification system 100 may assign each of the plurality of minutiaefrom the list of minutiae 412 into corresponding octant sectors withinthe set of octant sectors 432. The assigned minutiae may be associatedwith the corresponding octant sectors in a list 442 that includes thenumber of minutiae that are identified within each individual octantsector. For example, as shown in FIG. 4, the exemplary octant sector k₁has no identified minutiae, whereas the exemplary k₆ includes twoidentified minutiae within the octant sector. The graphical illustration444 represents the locations of the plurality of minutiae, relative tothe particular selected minutia, M_(i), within the individual octantsectors.

The process 400 may include identifying a neighboring minutiae to theparticular minutia for each octant sector (450). For instance, theautomatic fingerprint identification system 100 may identify, from allthe neighboring minutiae within each octant sector, the neighboringminutia that is the closest neighboring minutia based on the distancebetween each neighboring minutia and the particular selected minutia,M_(i). For example, for the octant sector k₆, the automatic fingerprintidentification system 100 may determine that the minutia, M₆ is theclosest neighboring minutia based on the distance between M_(i) and M₆.The closest neighboring minutiae for all of the octant sectors may beaggregated within a list of closest neighboring minutiae 452 thatidentifies each of the closest neighboring minutiae.

The process 400 ay include generating an octant feature vector for theparticular minutia (460). For instance, the automatic fingerprintidentification system 100 may generate an octant feature vector 462,based on the list of closest neighboring minutiae 452, which includes aset of relative features such as the Euclidean distance 230, the minimumrotation angle 240, and the minimum rotation angle 250 as describedpreviously with respect to FIG. 2.

As described above with respect to FIGS. 2-4, OFVs for minutiae may beused to characterize local relationships with neighboring minutiae,which are invariant to the rotation and translation of the fingerprintthat includes the minutiae. The OFVs are also insensitive to distortion,since the nearest neighboring minutiae are assigned to multiple octantsectors in various directions, thereby allowing flexibility oforientation of up to 45°. In this regard, the OFVs of minutiae within afingerprint may be compared against the OFVs of minutiae within anotherfingerprint (e.g., a search fingerprint) to determine a potential matchbetween the two fingerprints. Descriptions of the general fingerprintmatching process and the OFV matching process are provided below.

Fingerprint Identification and Matching

In general, the automatic fingerprint identification system 100 mayperform fingerprint identification and matching in two stages: (1) anenrollment stage, and (2) an identification/verification stage.

In the enrollment stage, an individual (or a “registrant”) has theirfingerprints and personal information enrolled. The registrant may be anindividual manually providing their fingerprints for scanning or,alternately, an individual whose fingerprints were obtained by othermeans. In some examples, registrants may enroll fingerprints usinglatent prints, libraries of fingerprints, and any other suitablerepositories and sources of fingerprints. As described, the process of“enrolling” and other related terms refer to providing biometricinformation (e.g., fingerprints) to an identification system (e.g., theautomatic fingerprint identification system 100).

The automatic fingerprint identification 100 system may extract featuressuch as minutiae from fingerprints. As described, “features” and relatedterms refer to characteristics of biometric information (e.g.,fingerprints) that may be used in matching, verification, andidentification processes. The automatic fingerprint identificationsystem 100 may create a reference record using the personal informationand the extracted features, and save the reference record into thedatabase 150 for subsequent fingerprint matching, verification, andidentification processes.

In some implementations, the automatic fingerprint identification system100 may contain millions of reference records. As a result, by enrollinga plurality of registrants (and their associated fingerprints andpersonal information), the automatic fingerprint identification system100 may create and store a library of reference records that may be usedfor comparison to search records. The library may be stored at thedatabase 150 associated.

In the identification stage, the automatic fingerprint identificationsystem 100 may use the extracted features and personal information togenerate a record known as a “search record”. The search recordrepresents a source fingerprint for which identification is sought. Forexample, in criminal investigations, a search record may be retrievedfrom a latent print at a crime scene. The automatic fingerprintidentification may compare the search record with the enrolled referencerecords in the database 150. For example, during a search procedure, asearch record may be compared against the reference records stored inthe database 150. In such an example, the features of the search recordmay be compared to the features of each of the plurality of referencerecords. For instance, minutiae extracted from the search record may becompared to minutiae extracted from each of the plurality of referencerecords.

As described, a “similarity score” is a measurement of the similarity ofbetween two or more elements (e.g., minutiae) belonging to a searchrecord and a reference record. The similarity score may be representedas a numerical value representative of a degree of similarity. Forinstance, in some implementations, the values of the similarity scoremay range from 0.0 to 1.0 or 0 to 100%, where a higher magnituderepresents a greater degree of similarity between the search record andthe reference record.

The automatic fingerprint identification system 100 may computeindividual similarity scores for each comparison of features (e.g.,minutiae), and aggregate similarity scores (or “final similarityscores”) between the search record to each of the plurality of referencerecords. In this regard, the automatic fingerprint identification system100 may generate similarity scores of varying levels of specificitythroughout the matching process of the search record and the pluralityof reference records.

The automatic fingerprint identification system 100 may also sort eachof the individual similarity scores based on the value of the respectivesimilarity scores of individual features. For instance, the automaticidentification system 100 may compute individual similarity scoresbetween respective minutiae between the search fingerprint and thereference fingerprint, and sort the individual similarity scores bytheir respective values.

A higher final similarity score indicates a greater overall similaritybetween the search record and a reference record while a lower finalsimilarity score indicates a lesser over similarity between the searchrecord and a reference record. Therefore, the match (e.g., therelationship between the search record and a reference record) with thehighest final similarity score is the match with the greatestrelationship (based on minutiae comparison) between the search recordand the reference record.

Minutiae and OFV Matching

Minutiae and corresponding OFV may be determined for fingerprints in areference record or in a search record. As described above, whenidentifying a match for a fingerprint, the fingerprint to be matched maybe input to the automatic fingerprint identification system 100 as aninput fingerprint 104. A search record may then be generated thatincludes the input fingerprint (also referred to as search fingerprint)and data indicative of any minutiae and OFVs in the search fingerprint.

The data indicative of any minutiae and OFVs in the search fingerprintmay be compared to minutiae and OFVs in a reference fingerprint toidentify mated minutiae pairs. As part of the comparison, transformationparameters may be estimated by comparing attributes of the correspondingmated minutiae. For example, the transformation parameters may indicatethe degree to which the search record has been transformed (e.g.,perturbed or twisted) as relative to a particular reference record. Inother examples, the transformation parameters may be applied to verifythat, for a particular pair of a reference record and a search record (a“potential matched fingerprint pair”), mated minutiae pairs exhibitcorresponding degrees of transformation.

In some implementations, the automatic fingerprint identification system100 may use the OFVs to determine the number of possible correspondingminutiae pairs. For example, the automatic fingerprint identificationsystem 100 may evaluate the similarity between two respective OFVsassociated with the search record and the reference record. Theautomatic fingerprint identification system 100 may identify allpossible local matching areas of the compared fingerprints by comparingthe OFVs. The automatic fingerprint identification system 100 may alsocalculate an individual similarity score for each of the mated OFVpairs. The automatic fingerprint identification system 100 may clusterall OFVs of the matched areas with similar transformation effects (e.g.,rotation and transposition) into a group.

Based on the amount of similarity between mated minutiae pairs in eachpotential matched fingerprint pair, and the consistency of thetransformation, a similarity score may be computed. An individualsimilarity score reflects a confidence that a particular minutiaecorresponds to a particular search minutiae that is being compared to.The automatic fingerprint identification system 100 may then computeaggregate similarity scores, between a list of particular minutiae and alist of search minutiae, based the values of the individual similarityscores for each minutiae. For instance, as described more particularlybelow, various types of aggregation techniques may be used to determinethe aggregate similarity scores between the reference fingerprint andthe search fingerprint. In some implementations, the pair of potentialmatched fingerprint pairs with the highest similarity score may bedetermined as a candidate matched fingerprint pair.

FIG. 5 illustrates an exemplary process of calculating an individualsimilarity score between a particular minutia and a search minutia.Referring to FIG. 5, a similarity determination process 500 may be usedto compute an individual similarity score between a particular minutia502 a from a reference fingerprint, and a search minutia 502 b from asearch fingerprint. A reference OFV 504 a and a search OFV 504 b may begenerated for the particular minutia 502 a and the search minutia 504 b,respectively, using the techniques described with respect to FIG. 4. Asshown, the search and reference OFVs 504 a and 504 b include individualoctant sectors k₀ to k₇ as described as illustrated in FIG. 3. Each ofthe reference OFV 504 a and the search OFV 504 b may include parameterssuch as, for example, the Euclidian distance 230, the minimum rotationangle 240, and the minimum rotation angle 250 as described with respectto FIG. 2. As shown in FIG. 5, exemplary parameters 506 a and 506 b mayrepresent the parameters for octant sector k₀ of the reference OFV 502 aand the search OFV 502 b, respectively.

The similarity score determination may be performed by an OFV comparisonmodule 520, which may be a software module or component of the automaticfingerprint identification system 100. In general, the similarity scorecalculation includes four operations. Initially, the Euclidian distancevalues of a particular octant sector may be evaluated (522).Corresponding sectors between the reference OFV 504 a and the similarityOFV 504 b may then be compared (524). A similarity score between aparticular octant sector within the reference OFV 504 a and itscorresponding octant sector in the search OFV 504 b may then be computed(526). The similarity scores for other octant sectors of the referenceOFV 504 a and the search OFV 504 b may then be computed and combined togenerate the final similarity score between the reference OFV 504 a andthe search OFV 504 b (528).

With respect to operation 522, the similarity module 520 may initiallydetermine if the Euclidian distance values within the parameters 506 aand 506 b are non-zero values. For instance, as shown in decision point522 a, the Euclidean distance associated with the octant sector of thereference OFV 504 a, d_(RO), is initially be evaluated. If this value isequal to zero, then the similarity score for the octant sector k₀ is setto zero. Alternatively, if the value of d_(RO) is greater than zero,then the similarity module 520 proceeds to decision point 522 b, wherethe Euclidean distance associated with the octant sector of the searchOFV 504 a, d_(SO), is evaluated. If the value of d_(SO) is not greaterthan zero, then the OFV similarity module 520 evaluates the value of theEuclidean distance d_(S1), which is included in an adjacent sector k₁ tothe octant sector k₀ within the reference OFV 504 b. Although FIG. 5represents only one of the adjacent sectors being selected, because eachoctant sector includes two adjacent octant sectors as shown in FIG. 3,in other implementations, octant sector k₇ may also be evaluated. If thevalue of the Euclidean distance within the adjacent octant sector is notgreater than zero, then the similarity module 520 sets the value ofindividual similarity score S_(RS01), between the octant sector k₀ ofthe reference OFV 504 a and the octant sector k₁ of the reference OFV504 a, to zero.

Alternatively, if the either the value of Euclidean distance d_(RO)within the octant sector k₀ of the reference OFV 504 a, or the Euclideandistance d_(S1) within the adjacent octant sector k₁ of the search OFV504 b is determined to be a non-zero value within the decision points522 b and 522 c, respectively, then the similarity module proceeds tostep 524.

In some instances, a particular octant vector may include zerocorresponding minutiae within the search OFV 504 b due to localizeddistortions within the search fingerprint. In such instances, where thecorresponding minutiae may have drifted to an adjacent octant sector,the similarity module 520 may alternatively compare the features of theoctant vector of the reference OFV 504 a to a corresponding adjacentoctant vector of the search OFV 504 b as shown in step 524 b.

If proceeding through decision point 522 b, the similarity module 520may proceed to step 524 a where the corresponding octant sectors betweenthe reference OFV 504 a and the search OFV 504 b are compared. Ifproceeding through decision point 522 c, the similarity module 520 mayproceed to step 524 b where the octant sector k₀ of the reference OFV504 a is compared to the corresponding adjacent octant sector k₁ thesearch OFV 504 b. During either process, the similarity module 520 maycompute the difference between the parameters that are included withineach octant sector of the respective OFVs. For instance, as shown, thedifference between the Euclidean distances 230, Δd, the differencebetween the minimum rotation angles 240, Δα, and the difference betweenthe minimum rotation angles 250, Δβ, may be computed. Since theseparameters represent geometric relationships between pairs of minutiae,the differences between them represent distance and orientationdifferences between the reference and search minutiae with respect toparticular octant sectors.

In some implementations, dynamic threshold values for the computedfeature differences may be used to handle nonlinear distortions withinthe search fingerprint in order to find mated minutiae between thesearch and reference fingerprint. For instance, the values of thedynamic thresholds may be adjusted to larger or smaller values to adjustthe sensitivity of the mated minutiae determination process. Forexample, if the value of the threshold for the Euclidean distance is setto a higher value, than more minutiae within a particular octant sectormay be determined to be a neighboring minutia to a particular minutiaebased on the distance being lower than the threshold value. Likewise, ifthe threshold is set to a lower value, then a smaller number of minutiaewithin the particular octant sector may be determined to be neighboringminutia based on the distance to the particular minutia being greaterthan the threshold value.

After either comparing the corresponding octant sectors in step 524 a orcomparing the corresponding adjacent octant sectors in step 524 b, thesimilarity module 520 may then compute an individual similarity scorebetween the respective octant sectors in steps 526 a and 526 b,respectively. For instance, the similarity score may be computed basedon the values of the feature differences as computed in steps 524 a and524 b. For instance, the similarity score may represent the featuredifferences and indicate minutiae that are likely to be distortedminutiae. For example, if the feature differences between a particularminutiae and corresponding search minutia within a particular octantsector are close the dynamic threshold values, the similarity module 520may identify the corresponding search minutia as a distortion candidate.

After computing the similarity score for either the corresponding octantsectors, or the corresponding adjacent sectors in steps 526 a and 526 b,respectively, the similarity module 520 may repeat the steps 522-526 forall of the other octant sectors included within the reference OFV 504 aand the search OFV 504 b. For instance, the similarity module 520 mayiteratively execute the steps 522-526 until the similarity scoresbetween each corresponding octant sector and each corresponding adjacentoctant sector are computed for the reference OFV 504 a and the searchOFV 504 b.

The similarity module may then combine the respective similarity scoresfor each corresponding octant sectors and/or the corresponding adjacentoctant sectors to generate a final similarity score between theparticular minutia and the corresponding search minutia. This finalsimilarity score is also referred to as the “individual similarityscore” between corresponding minutiae within the search and referencefingerprints as described in other sections of this specification. Theindividual similarity score indicates a strength of the local matchingof the corresponding OFV.

In some implementations, the particular aggregation technique used bythe similarity module 522 to generate the final similarity score (or the“individual similarity score”) may vary. For example, in some instances,the final similarity score may be computed based on adding the values ofthe similarity scores for the corresponding octant sectors and thecorresponding adjacent octant sectors, and normalizing the sum by a sumof a total number of possible mated minutiae for the particular minutiaand a total of number of possible mated minutiae for the search minutia.In this regard, the final similarity score is weighted by consideringthe number of mated minutiae and the total number of possible matedminutiae.

As described above, FIG. 5 illustrates a method utilized by theautomatic fingerprint identification system to process, analyze, andmatch individual minutiae from a search fingerprint to a referencefingerprint. As described further below, this method may be utilizedwithin a matching operation for a distorted fingerprint to compute afinal similarity score that indicates a confidence of a fingerprintmatch between a search fingerprint and a reference fingerprint.

Distorted Fingerprint Matching

FIGS. 6A and 6B illustrate an exemplary distorted fingerprint matchingoperation 600. The fingerprint matching operation 600 may be used tomatch a search fingerprint that may be nonlinearly distorted or mayexhibit other types of errors that would likely cause inaccurate resultsusing other fingerprint matching technologies. The fingerprint matchingoperation 600 employs the principles and techniques described previouslyin FIGS. 1-5 to reduce errors resulting from distortion.

The fingerprint matching operation 600 may include generating a list ofinvariant and distortion-tolerant reference OFVs 602 a for a list ofparticular minutiae 602 a, and a list of invariant anddistortion-toleration search OFVs 604 b for a list of search minutiae602 a. For instance, as described in FIG. 4, the list of reference OFVs604 a and the list of search OFVs 604 b may be generated by comparingeach minutia of the list of search minutiae 602 a and the list ofreference 602 b to its neighboring minutiae within a set of octantsectors.

An OFV comparison module may compare the respective search and referenceOFVs 604 a and 604 b, respectively, and generate a list of all possiblemated minutiae 612. The list of all possible mated minutiae may includeindividual pairs of search minutiae and corresponding reference minutiaebased on comparing the features included within the respective referenceOFVs included in the list of reference OFVs 604 a and the respectivesearch OFVs included in the list of search OFVs 604 b. The list of allpossible mated minutiae 812 may be ranked by similarity such that matedminutiae having a higher similarity are ranked higher.

In some implementations, the list of reference OFVs 604 a and the listof search OFVs 604 b may include a set of absolute features that improvefingerprint matching for distorted fingerprint matching. For instance,the absolute features may include a direction, x-y coordinates, aquality score, a ridge frequency, and a curvature. In someimplementations, one or more of the absolute features are included intothe calculation of individual similarity scores, as described in FIG. 5,as weights to factor in impacts of distortions on the searchfingerprint.

Next, a Grouping Module 620 of the automatic fingerprint identificationsystem 100 may group the listed possible minutiae pairs in differentgroups using a pose grouping technique (622). In the pose groupingtechnique, rigid transformation parameters (Δy_(i),Δx_(i),Δθ_(i)) aredetermined for each possible mated minutiae pair i using Equations 1-3noted below.

Δx _(i) =x _(i) ^(T) −x _(i) ^(I)  [Equation 1]

Δy _(i) =y _(i) ^(T) −y _(i) ^(I)  [Equation 2]

Δθ_(i)=θ_(i) ^(T)−θ_(i) ^(I)  [Equation 3]

For other mated pairs in which j≠i, the rigid transformation parameters(Δy_(j),Δx_(j),Δθ_(j)) are determined using Equations 4a-4c noted below.

$\{ {\begin{matrix}{{{{{\Delta \; x_{i}} - {\Delta \; x_{j}}}} < T_{1}}\mspace{256mu}} & \lbrack {{Equation}\mspace{14mu} 4a} \rbrack \\{{{{{\Delta \; y_{i}} - {\Delta \; y_{j}}}} < T_{2}}\mspace{250mu}} & \lbrack {{Equation}\mspace{14mu} 4b} \rbrack \\{{\min ( {{{{\Delta\theta}_{i} - {\Delta\theta}_{j}}},{180 - {{{\Delta\theta}_{i} - {\Delta\theta}_{j}}}}} )} < T_{3}} & \lbrack {{Equation}\mspace{14mu} 4c} \rbrack\end{matrix}\quad} $

T₁, T₂ and T₃ are thresholds that may be set by an administrator of theautomatic fingerprint identification system 100. Two rigidtransformation parameter sets are considered close to each other if theysatisfy the constraints set forth by Equations 4 a-4 c. Mated pairs jmay be removed from the list of possible minutiae pairs if their rigidtransformation parameters satisfy the constraints of Equations 4a-4c.

The Grouping Module 620 may repeat the calculation of the rigidtransformation parameters using Equations 1-4c for all i and j matedpairs. Based on the similarity between the calculated rigidtransformation parameters, the minutiae pairs may be divided into twogroups. Thus, two pairs of possible mated minutiae may be grouped into asingle group if the rigid transformation parameters of the two pairs arewithin a threshold range of similarity to each other. Each group ofpossible mated minutiae contains a set of possible mated minutiae pairsthat are subject to similar rigid transformation.

After completing the pose grouping, the rigid geometric constraints areused to find a set of geometrically consistent pairs for each group. Inparticular, for each group of possible mated minutiae pairs, the twobest minutiae pairs may be selected as a reference pair and more matedpairs may be identified from the complete list using the rigid geometricconstraints as described above. A similarity score between all theminutiae pairs in a group may then be determined and averaged. Thescored groups may be sorted based on their respective average similarityscores 624. For example, groups having a higher average similarity scoremay be ranked higher.

An example of dividing minutiae pairs into two groups for reference andsearch fingerprints is shown in FIGS. 7 and 8. FIG. 7 depicts an exampleof a group (“Group A”) in which a reference fingerprint (image (b)) anda search fingerprint (image (a)) have nine mated minutiae M0-M8 in agroup. Mated minutiae pairs have been marked up in square boxes foremphasis and illustrative purposes. Image (c) in FIG. 7 depicts thetransformed search minutiae superimposed on the reference minutiae. Therigid transformation (Δx,Δy,Δθ) is (42, 9, 10). The ovals in images (a)and (b) correspond to ovals in image (c). As can be seen in FIG. 7, themated minutiae M0-M8 only cover a portion of the fingerprint.Accordingly, even if non-linear transformation parameters are estimatedfrom mated minutiae pairs M0-M8, the non-linear transformation mayresult in an accurate transformation only in the area close to the matedminutiae pairs M0-M8. The top part of the fingerprints corresponding tothe areas marked by ovals may still be relatively displaced after anon-linear transformation that relies on mated minutiae pairs M0-M8.

FIG. 8 depicts an example of a grouping (“Group B”) of five matedminutiae pairs between the reference fingerprint (image (b)) and asearch fingerprint (image (a)). Mated minutiae pairs have been marked upin square boxes for emphasis and illustrative purposes. The rigidtransformation (Δx,Δy,Δθ) of the group of mated minutiae is (59, 32,−22). The mated minutiae pairs of Group B may have a similar issue asthe mated minutiae pairs of Group A in that the pairs are only locatedin a particular region of the fingerprint and non-linear transformationmay result in an accurate transformation only in the area close to themated minutiae pairs.

As described above, the two best minutiae pairs of Groups A and B,respectively, may be selected as a reference pair and more mated pairsmay be identified from the complete list using the rigid geometricconstraints. A similarity score between all the minutiae pairs in GroupsA and B may be determined and averaged. Groups A and B may then beranked according to their respective average similarity score.

Next, the grouping module 620 may combine two groups if the topology ofthe two groups is similar. For example, the grouping module 620 may gothrough the list of available groups and compare the topology of twogroups in the list. If the similarity in topology of the two groupssatisfies topological constraints, the two groups may be combined toform one larger group 626. In some implementations, the grouping module630 may begin at the top of the list of groups ranked by similarity andgo down the list of groups to identify pairs of groups that have similartopologies and can be combined to form a larger group.

FIG. 9 depicts an example in which portions of two groups may becombined. In FIG. 9, minutiae belonging to Group 1 are included in thelarger oval. Minutiae belonging to Group 2 are included in the smalleroval. Minutiae belonging to a reference footprint are depicted in solidblack circles. Minutiae belonging to a search footprint are depicted insolid grey circles. Groups 1 and 2, respectively, include mated minutiaepairs comprising minutiae from the reference footprint and minutiae fromthe search footprint. As an example, C_(i) ^(T)↔C_(i) ^(I) and C_(j)^(T)↔C_(j) ^(I) are mated minutiae pairs in Group 1, and C_(k)^(T)↔C_(k) ^(I) is a mated minutiae pair in Group 2.

The minutiae pair C_(k) ^(T)↔C_(k) ^(I) may be joined to Group 1 iftopological constraints are satisfied. The topological constraint usedis the cross product between two vectors C_(i) ^(T)-C_(j) ^(T) and C_(k)^(T)-C_(j) ^(T), and two vectors C_(i) ^(I)-C_(j) ^(I) and C_(k)^(I)-C_(j) ^(I). If the cross product points to the same direction orwithin a threshold range of the same direction, it is topologicallyconsistent. The same procedure is repeated for every pair in Group 1. Ifall of the constraints are satisfied, the minutiae pair C_(k) ^(T)↔C_(k)^(I) is added to group 1. Merged groups may be distinguished though anysuitable identification means such as, for example, a tag or metadataindicating that a group is a merged one.

After processing all the groups and combining groups that can becombined if the constraints noted above are satisfied 630, an AlignmentModule 640 of the automatic fingerprint identification system 100 mayexamine each group and determine whether the group is a merged group ora non-merged group. The matched minutiae in the merged group are used toestimate parameters of a non-linear transformation model. The non-lineartransformation may be used to align the reference fingerprint with thesearch fingerprint.

Since mated minutiae pairs in a merged group are not geometricallyconsistent with each other with respect to the rigid transformation,non-linear transformation may be used for better alignment. Non-lineartransformation parameters for mated minutiae pairs may be determinedusing various suitable techniques, including, for example, a Thin-platespline (TPS) model. Accordingly, in some implementations, (TPS)parameters may be estimated from the matched minutiae pairs in themerged match groups, and TPS transformation may be applied to searchfingerprint minutiae so that the minutiae in the search fingerprint arebetter aligned with the minutiae in the reference fingerprint. The TPSparameters, or more generally, the non-linear transformation parameters,are applied to each of the search minutiae of search print, not just thesearch minutiae in the merged group of search print.

FIG. 10 illustrates an example of the alignment of a referencefingerprint and a search fingerprint after applying non-lineartransformation parameters determined using the TPS method. Matedminutiae pairs have been marked up in square boxes for emphasis andillustrative purposes. Image (c) in FIG. 10 depicts the transformedsearch minutiae superimposed on the reference minutiae. The ovals inimages (a) and (b) correspond to the oval in image (c)

In FIG. 10, groups A and B, as respectively shown in FIGS. 7 and 8, havebeen merged resulting in a combined group of 14 mated minutiae M0-M13.By combining two groups and performing non-linear transformation on thesearch minutiae, the alignment and matching between the searchfingerprint and reference fingerprint is significantly improved over thealignment and matching of mated minutiae pairs shown in FIGS. 7 and 8.

After performing the non-linear transformation on the minutiae of thesearch fingerprint, a similarity module 650 may again conduct asimilarity analysis of all the minutiae (mated and non-mated) for thereference and search fingerprints 654. In some implementations, thesimilarity levels are determined for matched and non-matched minutiae inan overlapping area of the search minutiae and the reference minutiae.

As described above with reference to FIG. 5, an individual similarityscore may be computed based on aggregating single similarity scoresbetween individual octant sectors of the respective OFVs of the searchand particular minutia within mated and non-mated minutiae pairs. Thesimilarity score calculation may additionally include weights based onthe absolute features included within the respective OFVs for the searchand reference minutiae. The list of individual similarity scores for allminutiae may then be aggregated to compute a final similarity scorebetween the reference fingerprint and the search fingerprint. In someimplementations, the final similarity score is determined based onselecting the maximum value of the similarity score among alltopologically consistent group pairs. For instance, the final similarityscore may be the best similarity level among the merged groups.

While this specification contains many specifics, these should not beconstrued as limitations on the scope of the disclosure or of what maybe claimed, but rather as descriptions of features specific toparticular embodiments. Certain features that are described in thisspecification in the context of separate embodiments may also beimplemented in combination in a single embodiment. Conversely, variousfeatures that are described in the context of a single embodiment mayalso be implemented in multiple embodiments separately or in anysuitable sub-combination. Moreover, although features may be describedabove as acting in certain combinations and may even be claimed as such,one or more features from a claimed combination may in some cases, beexcised from the combination, and the claimed combination may bedirected to a sub-combination or variation of a sub-combination.

Similarly, while actions are depicted in the drawings in a particularorder, this should not be understood as requiring that such actions beperformed in the particular order shown or in sequential order, or thatall illustrated actions be performed, to achieve desirable results.Moreover, the separation of various system components in the embodimentsdescribed above should not be understood as requiring such separation inall embodiments, and it should be understood that the described programcomponents and systems may generally be integrated together in a singlesoftware product or packaged into multiple software products.

It should be understood that the phrase one or more of and the phrase atleast one of include any combination of elements. For example, thephrase one or more of A and B includes A, B, or both A and B. Similarly,the phrase at least one of A and B includes A, B, or both A and B.

Thus, particular implementations have been described. Otherimplementations are within the scope of the following claims. Forexample, the actions recited in the claims may be performed in adifferent order and still achieve desirable results.

What is claimed is:
 1. A computer-implemented method to match distortedfingerprints, the computer-implemented method comprising: selecting (i)one or more search minutiae of a search fingerprint, and (ii) one ormore reference minutiae of a reference fingerprint; for each searchminutia included in the one or more search minutiae, identifying acorresponding reference minutia from the one or more reference minutiae,the corresponding reference minutia having a similarity to the searchminutia that satisfies a similarity threshold; determining, by one ormore processors, one or more groups of the one or more search minutiaein the search fingerprint and the one or more reference minutiae in thereference fingerprint that match the each other; determining, by the oneor more processors, one or more matches between the groups based on atopological consistency between two groups; for each matched pair ofgroups, merging, by the one or more processors, minutiae in the pair ofgroups; and performing, by the one or more processors, a non-lineartransformation on the one or more search minutiae of the searchfingerprint.
 2. The computer-implemented method of claim 1, furthercomprising: in response to performing the non-linear transformation,determining similarity levels associated with the selected one or moresearch minutiae and the selected one or more reference minutiae, thesimilarity levels including similarities of matched and non-matchedminutiae in an overlapping area of the selected one or more searchminutiae and the selected one or more reference minutiae; anddetermining, as a similarity between the search fingerprint and thereference fingerprint, the best similarity level among all groups havingtopologically consistent group pairs.
 3. The computer-implemented methodof claim 1, wherein performing a non-linear transformation comprises:determining parameters for a Thin-Plate Spline (TPS) model; and applyingthe determined parameters to the one or more search minutiae of thesearch fingerprint to perform the non-linear transformation.
 4. Thecomputer-implemented method of claim 1, further comprising: determiningwhether a group is a merged group or a non-merged group; and in responseto determining that the group is a non-merged group, performing rigidtransformation on the minutiae included in the group.
 5. Thecomputer-implemented method of claim 4, further comprising: determiningthat the group is a merged group, wherein performing the non-lineartransformation comprises: performing non-linear transformation on theone or more search minutiae of the search fingerprint in response todetermining that the group is a merged group.
 6. Thecomputer-implemented method of claim 1, wherein each group includes twoor more mated minutiae pairs having rigid transformation parameters thatsatisfy a threshold level of similarity.
 7. The computer-implementedmethod of claim 6, wherein the one or more groups of the one or moresearch minutiae in the search fingerprint and the one or more referenceminutiae in the reference fingerprint are determined based on values ofthe rigid transformation parameters.
 8. A system comprising: one or moreprocessors and one or more storage devices storing instructions that areoperable and when executed by one or more processors, cause the one ormore processors to perform operations comprising: selecting (i) one ormore search minutiae of a search fingerprint, and (ii) one or morereference minutiae of a reference fingerprint; for each search minutiaincluded in the one or more search minutiae, identifying a correspondingreference minutia from the one or more reference minutiae, thecorresponding reference minutia having a similarity to the searchminutia that satisfies a similarity threshold; determining one or moregroups of the one or more search minutiae in the search fingerprint andthe one or more reference minutiae in the reference fingerprint thatmatch the each other; determining one or more matches between the groupsbased on a topological consistency between two groups; for each matchedpair of groups, merging, by the one or more processors, minutiae in thepair of groups; and performing a non-linear transformation on the one ormore search minutiae of the search fingerprint.
 9. The system of claim8, wherein the operations further comprise: in response to performingthe non-linear transformation, determining similarity levels associatedwith the selected one or more search minutiae and the selected one ormore reference minutiae, the similarity levels including similarities ofmatched and non-matched minutiae in an overlapping area of the selectedone or more search minutiae and the selected one or more referenceminutiae; and determining, as a similarity between the searchfingerprint and the reference fingerprint, the best similarity levelamong all groups having topologically consistent group pairs.
 10. Thesystem of claim 8, wherein performing a non-linear transformationcomprises: determining parameters for a Thin-Plate Spline (TPS) model;and applying the determined parameters to the one or more searchminutiae of the search fingerprint to perform the non-lineartransformation.
 11. The system of claim 8, wherein the operationsfurther comprise: determining whether a group is a merged group or anon-merged group; and in response to determining that the group is anon-merged group, performing rigid transformation on the minutiaeincluded in the group.
 12. The system of claim 11, wherein: theoperations further comprise: determining that the group is a mergedgroup, performing the non-linear transformation comprises: performingnon-linear transformation on the one or more search minutiae of thesearch fingerprint in response to determining that the group is a mergedgroup.
 13. The system of claim 8, wherein each group includes two ormore mated minutiae pairs having rigid transformation parameters thatsatisfy a threshold level of similarity.
 14. The system of claim 13,wherein the one or more groups of the one or more search minutiae in thesearch fingerprint and the one or more reference minutiae in thereference fingerprint are determined based on values of the rigidtransformation parameters.
 15. One or more non-transitorycomputer-readable storage media comprising instructions, which, whenexecuted by one or more processors, cause the one or more processors toperform operations comprising: selecting (i) one or more search minutiaeof a search fingerprint, and (ii) one or more reference minutiae of areference fingerprint; for each search minutia included in the one ormore search minutiae, identifying a corresponding reference minutia fromthe one or more reference minutiae, the corresponding reference minutiahaving a similarity to the search minutia that satisfies a similaritythreshold; determining one or more groups of the one or more searchminutiae in the search fingerprint and the one or more referenceminutiae in the reference fingerprint that match the each other;determining one or more matches between the groups based on atopological consistency between two groups; for each matched pair ofgroups, merging, by the one or more processors, minutiae in the pair ofgroups; and performing a non-linear transformation on the one or moresearch minutiae of the search fingerprint.
 16. The one or morenon-transitory computer-readable storage media of claim 15, wherein theoperations further comprise: in response to performing the non-lineartransformation, determining similarity levels associated with theselected one or more search minutiae and the selected one or morereference minutiae, the similarity levels including similarities ofmatched and non-matched minutiae in an overlapping area of the selectedone or more search minutiae and the selected one or more referenceminutiae; and determining, as a similarity between the searchfingerprint and the reference fingerprint, the best similarity levelamong all groups having topologically consistent group pairs.
 17. Theone or more non-transitory computer-readable storage media of claim 16,wherein performing a non-linear transformation comprises: determiningparameters for a Thin-Plate Spline (TPS) model; and applying thedetermined parameters to the one or more search minutiae of the searchfingerprint to perform the non-linear transformation.
 18. The one ormore non-transitory computer-readable storage media of claim 15, whereinthe operations further comprise: determining whether a group is a mergedgroup or a non-merged group; and in response to determining that thegroup is a non-merged group, performing rigid transformation on theminutiae included in the group.
 19. The one or more non-transitorycomputer-readable storage media of claim 18, wherein: the operationsfurther comprise: determining that the group is a merged group,performing the non-linear transformation comprises: performingnon-linear transformation on the one or more search minutiae of thesearch fingerprint in response to determining that the group is a mergedgroup.
 20. The one or more non-transitory computer-readable storagemedia of claim 15, wherein each group includes two or more matedminutiae pairs having rigid transformation parameters that satisfy athreshold level of similarity.